# Properties

 Label 825.2.k.d.518.1 Level $825$ Weight $2$ Character 825.518 Analytic conductor $6.588$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.58765816676$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 518.1 Root $$-1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 825.518 Dual form 825.2.k.d.782.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.22474 - 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} -3.00000i q^{6} +(2.44949 - 2.44949i) q^{7} +(-1.22474 + 1.22474i) q^{8} +3.00000i q^{9} +O(q^{10})$$ $$q+(-1.22474 - 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} -3.00000i q^{6} +(2.44949 - 2.44949i) q^{7} +(-1.22474 + 1.22474i) q^{8} +3.00000i q^{9} -1.00000i q^{11} +(-1.22474 + 1.22474i) q^{12} +(-2.44949 - 2.44949i) q^{13} -6.00000 q^{14} +5.00000 q^{16} +(-4.89898 - 4.89898i) q^{17} +(3.67423 - 3.67423i) q^{18} -2.00000i q^{19} +6.00000 q^{21} +(-1.22474 + 1.22474i) q^{22} +(4.89898 - 4.89898i) q^{23} -3.00000 q^{24} +6.00000i q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.44949 + 2.44949i) q^{28} +6.00000 q^{29} +4.00000 q^{31} +(-3.67423 - 3.67423i) q^{32} +(1.22474 - 1.22474i) q^{33} +12.0000i q^{34} -3.00000 q^{36} +(-2.44949 + 2.44949i) q^{38} -6.00000i q^{39} +6.00000i q^{41} +(-7.34847 - 7.34847i) q^{42} +(-7.34847 - 7.34847i) q^{43} +1.00000 q^{44} -12.0000 q^{46} +(4.89898 + 4.89898i) q^{47} +(6.12372 + 6.12372i) q^{48} -5.00000i q^{49} -12.0000i q^{51} +(2.44949 - 2.44949i) q^{52} +(4.89898 - 4.89898i) q^{53} +9.00000 q^{54} +6.00000i q^{56} +(2.44949 - 2.44949i) q^{57} +(-7.34847 - 7.34847i) q^{58} +2.00000 q^{61} +(-4.89898 - 4.89898i) q^{62} +(7.34847 + 7.34847i) q^{63} -1.00000i q^{64} -3.00000 q^{66} +(2.44949 - 2.44949i) q^{67} +(4.89898 - 4.89898i) q^{68} +12.0000 q^{69} -12.0000i q^{71} +(-3.67423 - 3.67423i) q^{72} +(2.44949 + 2.44949i) q^{73} +2.00000 q^{76} +(-2.44949 - 2.44949i) q^{77} +(-7.34847 + 7.34847i) q^{78} -10.0000i q^{79} -9.00000 q^{81} +(7.34847 - 7.34847i) q^{82} +(7.34847 - 7.34847i) q^{83} +6.00000i q^{84} +18.0000i q^{86} +(7.34847 + 7.34847i) q^{87} +(1.22474 + 1.22474i) q^{88} -12.0000 q^{89} -12.0000 q^{91} +(4.89898 + 4.89898i) q^{92} +(4.89898 + 4.89898i) q^{93} -12.0000i q^{94} -9.00000i q^{96} +(-9.79796 + 9.79796i) q^{97} +(-6.12372 + 6.12372i) q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + O(q^{10})$$ $$4 q - 24 q^{14} + 20 q^{16} + 24 q^{21} - 12 q^{24} + 24 q^{29} + 16 q^{31} - 12 q^{36} + 4 q^{44} - 48 q^{46} + 36 q^{54} + 8 q^{61} - 12 q^{66} + 48 q^{69} + 8 q^{76} - 36 q^{81} - 48 q^{89} - 48 q^{91} + 12 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$$.

 $$n$$ $$376$$ $$551$$ $$727$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.22474 1.22474i −0.866025 0.866025i 0.126004 0.992030i $$-0.459785\pi$$
−0.992030 + 0.126004i $$0.959785\pi$$
$$3$$ 1.22474 + 1.22474i 0.707107 + 0.707107i
$$4$$ 1.00000i 0.500000i
$$5$$ 0 0
$$6$$ 3.00000i 1.22474i
$$7$$ 2.44949 2.44949i 0.925820 0.925820i −0.0716124 0.997433i $$-0.522814\pi$$
0.997433 + 0.0716124i $$0.0228145\pi$$
$$8$$ −1.22474 + 1.22474i −0.433013 + 0.433013i
$$9$$ 3.00000i 1.00000i
$$10$$ 0 0
$$11$$ 1.00000i 0.301511i
$$12$$ −1.22474 + 1.22474i −0.353553 + 0.353553i
$$13$$ −2.44949 2.44949i −0.679366 0.679366i 0.280491 0.959857i $$-0.409503\pi$$
−0.959857 + 0.280491i $$0.909503\pi$$
$$14$$ −6.00000 −1.60357
$$15$$ 0 0
$$16$$ 5.00000 1.25000
$$17$$ −4.89898 4.89898i −1.18818 1.18818i −0.977571 0.210606i $$-0.932456\pi$$
−0.210606 0.977571i $$-0.567544\pi$$
$$18$$ 3.67423 3.67423i 0.866025 0.866025i
$$19$$ 2.00000i 0.458831i −0.973329 0.229416i $$-0.926318\pi$$
0.973329 0.229416i $$-0.0736815\pi$$
$$20$$ 0 0
$$21$$ 6.00000 1.30931
$$22$$ −1.22474 + 1.22474i −0.261116 + 0.261116i
$$23$$ 4.89898 4.89898i 1.02151 1.02151i 0.0217443 0.999764i $$-0.493078\pi$$
0.999764 0.0217443i $$-0.00692196\pi$$
$$24$$ −3.00000 −0.612372
$$25$$ 0 0
$$26$$ 6.00000i 1.17670i
$$27$$ −3.67423 + 3.67423i −0.707107 + 0.707107i
$$28$$ 2.44949 + 2.44949i 0.462910 + 0.462910i
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −3.67423 3.67423i −0.649519 0.649519i
$$33$$ 1.22474 1.22474i 0.213201 0.213201i
$$34$$ 12.0000i 2.05798i
$$35$$ 0 0
$$36$$ −3.00000 −0.500000
$$37$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$38$$ −2.44949 + 2.44949i −0.397360 + 0.397360i
$$39$$ 6.00000i 0.960769i
$$40$$ 0 0
$$41$$ 6.00000i 0.937043i 0.883452 + 0.468521i $$0.155213\pi$$
−0.883452 + 0.468521i $$0.844787\pi$$
$$42$$ −7.34847 7.34847i −1.13389 1.13389i
$$43$$ −7.34847 7.34847i −1.12063 1.12063i −0.991647 0.128984i $$-0.958828\pi$$
−0.128984 0.991647i $$-0.541172\pi$$
$$44$$ 1.00000 0.150756
$$45$$ 0 0
$$46$$ −12.0000 −1.76930
$$47$$ 4.89898 + 4.89898i 0.714590 + 0.714590i 0.967492 0.252902i $$-0.0813851\pi$$
−0.252902 + 0.967492i $$0.581385\pi$$
$$48$$ 6.12372 + 6.12372i 0.883883 + 0.883883i
$$49$$ 5.00000i 0.714286i
$$50$$ 0 0
$$51$$ 12.0000i 1.68034i
$$52$$ 2.44949 2.44949i 0.339683 0.339683i
$$53$$ 4.89898 4.89898i 0.672927 0.672927i −0.285463 0.958390i $$-0.592147\pi$$
0.958390 + 0.285463i $$0.0921474\pi$$
$$54$$ 9.00000 1.22474
$$55$$ 0 0
$$56$$ 6.00000i 0.801784i
$$57$$ 2.44949 2.44949i 0.324443 0.324443i
$$58$$ −7.34847 7.34847i −0.964901 0.964901i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ −4.89898 4.89898i −0.622171 0.622171i
$$63$$ 7.34847 + 7.34847i 0.925820 + 0.925820i
$$64$$ 1.00000i 0.125000i
$$65$$ 0 0
$$66$$ −3.00000 −0.369274
$$67$$ 2.44949 2.44949i 0.299253 0.299253i −0.541468 0.840721i $$-0.682131\pi$$
0.840721 + 0.541468i $$0.182131\pi$$
$$68$$ 4.89898 4.89898i 0.594089 0.594089i
$$69$$ 12.0000 1.44463
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i −0.702109 0.712069i $$-0.747758\pi$$
0.702109 0.712069i $$-0.252242\pi$$
$$72$$ −3.67423 3.67423i −0.433013 0.433013i
$$73$$ 2.44949 + 2.44949i 0.286691 + 0.286691i 0.835770 0.549079i $$-0.185021\pi$$
−0.549079 + 0.835770i $$0.685021\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ −2.44949 2.44949i −0.279145 0.279145i
$$78$$ −7.34847 + 7.34847i −0.832050 + 0.832050i
$$79$$ 10.0000i 1.12509i −0.826767 0.562544i $$-0.809823\pi$$
0.826767 0.562544i $$-0.190177\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 7.34847 7.34847i 0.811503 0.811503i
$$83$$ 7.34847 7.34847i 0.806599 0.806599i −0.177518 0.984118i $$-0.556807\pi$$
0.984118 + 0.177518i $$0.0568069\pi$$
$$84$$ 6.00000i 0.654654i
$$85$$ 0 0
$$86$$ 18.0000i 1.94099i
$$87$$ 7.34847 + 7.34847i 0.787839 + 0.787839i
$$88$$ 1.22474 + 1.22474i 0.130558 + 0.130558i
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ −12.0000 −1.25794
$$92$$ 4.89898 + 4.89898i 0.510754 + 0.510754i
$$93$$ 4.89898 + 4.89898i 0.508001 + 0.508001i
$$94$$ 12.0000i 1.23771i
$$95$$ 0 0
$$96$$ 9.00000i 0.918559i
$$97$$ −9.79796 + 9.79796i −0.994832 + 0.994832i −0.999987 0.00515471i $$-0.998359\pi$$
0.00515471 + 0.999987i $$0.498359\pi$$
$$98$$ −6.12372 + 6.12372i −0.618590 + 0.618590i
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ 18.0000i 1.79107i 0.444994 + 0.895533i $$0.353206\pi$$
−0.444994 + 0.895533i $$0.646794\pi$$
$$102$$ −14.6969 + 14.6969i −1.45521 + 1.45521i
$$103$$ −2.44949 2.44949i −0.241355 0.241355i 0.576055 0.817411i $$-0.304591\pi$$
−0.817411 + 0.576055i $$0.804591\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ 2.44949 + 2.44949i 0.236801 + 0.236801i 0.815524 0.578723i $$-0.196449\pi$$
−0.578723 + 0.815524i $$0.696449\pi$$
$$108$$ −3.67423 3.67423i −0.353553 0.353553i
$$109$$ 10.0000i 0.957826i −0.877862 0.478913i $$-0.841031\pi$$
0.877862 0.478913i $$-0.158969\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 12.2474 12.2474i 1.15728 1.15728i
$$113$$ −4.89898 + 4.89898i −0.460857 + 0.460857i −0.898936 0.438079i $$-0.855659\pi$$
0.438079 + 0.898936i $$0.355659\pi$$
$$114$$ −6.00000 −0.561951
$$115$$ 0 0
$$116$$ 6.00000i 0.557086i
$$117$$ 7.34847 7.34847i 0.679366 0.679366i
$$118$$ 0 0
$$119$$ −24.0000 −2.20008
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ −2.44949 2.44949i −0.221766 0.221766i
$$123$$ −7.34847 + 7.34847i −0.662589 + 0.662589i
$$124$$ 4.00000i 0.359211i
$$125$$ 0 0
$$126$$ 18.0000i 1.60357i
$$127$$ −2.44949 + 2.44949i −0.217357 + 0.217357i −0.807384 0.590027i $$-0.799117\pi$$
0.590027 + 0.807384i $$0.299117\pi$$
$$128$$ −8.57321 + 8.57321i −0.757772 + 0.757772i
$$129$$ 18.0000i 1.58481i
$$130$$ 0 0
$$131$$ 12.0000i 1.04844i −0.851581 0.524222i $$-0.824356\pi$$
0.851581 0.524222i $$-0.175644\pi$$
$$132$$ 1.22474 + 1.22474i 0.106600 + 0.106600i
$$133$$ −4.89898 4.89898i −0.424795 0.424795i
$$134$$ −6.00000 −0.518321
$$135$$ 0 0
$$136$$ 12.0000 1.02899
$$137$$ 9.79796 + 9.79796i 0.837096 + 0.837096i 0.988476 0.151380i $$-0.0483716\pi$$
−0.151380 + 0.988476i $$0.548372\pi$$
$$138$$ −14.6969 14.6969i −1.25109 1.25109i
$$139$$ 22.0000i 1.86602i 0.359856 + 0.933008i $$0.382826\pi$$
−0.359856 + 0.933008i $$0.617174\pi$$
$$140$$ 0 0
$$141$$ 12.0000i 1.01058i
$$142$$ −14.6969 + 14.6969i −1.23334 + 1.23334i
$$143$$ −2.44949 + 2.44949i −0.204837 + 0.204837i
$$144$$ 15.0000i 1.25000i
$$145$$ 0 0
$$146$$ 6.00000i 0.496564i
$$147$$ 6.12372 6.12372i 0.505076 0.505076i
$$148$$ 0 0
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 2.44949 + 2.44949i 0.198680 + 0.198680i
$$153$$ 14.6969 14.6969i 1.18818 1.18818i
$$154$$ 6.00000i 0.483494i
$$155$$ 0 0
$$156$$ 6.00000 0.480384
$$157$$ −9.79796 + 9.79796i −0.781962 + 0.781962i −0.980162 0.198199i $$-0.936491\pi$$
0.198199 + 0.980162i $$0.436491\pi$$
$$158$$ −12.2474 + 12.2474i −0.974355 + 0.974355i
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 24.0000i 1.89146i
$$162$$ 11.0227 + 11.0227i 0.866025 + 0.866025i
$$163$$ 12.2474 + 12.2474i 0.959294 + 0.959294i 0.999203 0.0399091i $$-0.0127068\pi$$
−0.0399091 + 0.999203i $$0.512707\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −18.0000 −1.39707
$$167$$ 2.44949 + 2.44949i 0.189547 + 0.189547i 0.795500 0.605953i $$-0.207208\pi$$
−0.605953 + 0.795500i $$0.707208\pi$$
$$168$$ −7.34847 + 7.34847i −0.566947 + 0.566947i
$$169$$ 1.00000i 0.0769231i
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ 7.34847 7.34847i 0.560316 0.560316i
$$173$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$174$$ 18.0000i 1.36458i
$$175$$ 0 0
$$176$$ 5.00000i 0.376889i
$$177$$ 0 0
$$178$$ 14.6969 + 14.6969i 1.10158 + 1.10158i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 14.6969 + 14.6969i 1.08941 + 1.08941i
$$183$$ 2.44949 + 2.44949i 0.181071 + 0.181071i
$$184$$ 12.0000i 0.884652i
$$185$$ 0 0
$$186$$ 12.0000i 0.879883i
$$187$$ −4.89898 + 4.89898i −0.358249 + 0.358249i
$$188$$ −4.89898 + 4.89898i −0.357295 + 0.357295i
$$189$$ 18.0000i 1.30931i
$$190$$ 0 0
$$191$$ 24.0000i 1.73658i 0.496058 + 0.868290i $$0.334780\pi$$
−0.496058 + 0.868290i $$0.665220\pi$$
$$192$$ 1.22474 1.22474i 0.0883883 0.0883883i
$$193$$ 7.34847 + 7.34847i 0.528954 + 0.528954i 0.920261 0.391306i $$-0.127977\pi$$
−0.391306 + 0.920261i $$0.627977\pi$$
$$194$$ 24.0000 1.72310
$$195$$ 0 0
$$196$$ 5.00000 0.357143
$$197$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$198$$ −3.67423 3.67423i −0.261116 0.261116i
$$199$$ 4.00000i 0.283552i −0.989899 0.141776i $$-0.954719\pi$$
0.989899 0.141776i $$-0.0452813\pi$$
$$200$$ 0 0
$$201$$ 6.00000 0.423207
$$202$$ 22.0454 22.0454i 1.55111 1.55111i
$$203$$ 14.6969 14.6969i 1.03152 1.03152i
$$204$$ 12.0000 0.840168
$$205$$ 0 0
$$206$$ 6.00000i 0.418040i
$$207$$ 14.6969 + 14.6969i 1.02151 + 1.02151i
$$208$$ −12.2474 12.2474i −0.849208 0.849208i
$$209$$ −2.00000 −0.138343
$$210$$ 0 0
$$211$$ 26.0000 1.78991 0.894957 0.446153i $$-0.147206\pi$$
0.894957 + 0.446153i $$0.147206\pi$$
$$212$$ 4.89898 + 4.89898i 0.336463 + 0.336463i
$$213$$ 14.6969 14.6969i 1.00702 1.00702i
$$214$$ 6.00000i 0.410152i
$$215$$ 0 0
$$216$$ 9.00000i 0.612372i
$$217$$ 9.79796 9.79796i 0.665129 0.665129i
$$218$$ −12.2474 + 12.2474i −0.829502 + 0.829502i
$$219$$ 6.00000i 0.405442i
$$220$$ 0 0
$$221$$ 24.0000i 1.61441i
$$222$$ 0 0
$$223$$ −17.1464 17.1464i −1.14821 1.14821i −0.986905 0.161305i $$-0.948430\pi$$
−0.161305 0.986905i $$-0.551570\pi$$
$$224$$ −18.0000 −1.20268
$$225$$ 0 0
$$226$$ 12.0000 0.798228
$$227$$ 12.2474 + 12.2474i 0.812892 + 0.812892i 0.985066 0.172175i $$-0.0550794\pi$$
−0.172175 + 0.985066i $$0.555079\pi$$
$$228$$ 2.44949 + 2.44949i 0.162221 + 0.162221i
$$229$$ 10.0000i 0.660819i 0.943838 + 0.330409i $$0.107187\pi$$
−0.943838 + 0.330409i $$0.892813\pi$$
$$230$$ 0 0
$$231$$ 6.00000i 0.394771i
$$232$$ −7.34847 + 7.34847i −0.482451 + 0.482451i
$$233$$ −4.89898 + 4.89898i −0.320943 + 0.320943i −0.849129 0.528186i $$-0.822872\pi$$
0.528186 + 0.849129i $$0.322872\pi$$
$$234$$ −18.0000 −1.17670
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 12.2474 12.2474i 0.795557 0.795557i
$$238$$ 29.3939 + 29.3939i 1.90532 + 1.90532i
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 1.22474 + 1.22474i 0.0787296 + 0.0787296i
$$243$$ −11.0227 11.0227i −0.707107 0.707107i
$$244$$ 2.00000i 0.128037i
$$245$$ 0 0
$$246$$ 18.0000 1.14764
$$247$$ −4.89898 + 4.89898i −0.311715 + 0.311715i
$$248$$ −4.89898 + 4.89898i −0.311086 + 0.311086i
$$249$$ 18.0000 1.14070
$$250$$ 0 0
$$251$$ 12.0000i 0.757433i 0.925513 + 0.378717i $$0.123635\pi$$
−0.925513 + 0.378717i $$0.876365\pi$$
$$252$$ −7.34847 + 7.34847i −0.462910 + 0.462910i
$$253$$ −4.89898 4.89898i −0.307996 0.307996i
$$254$$ 6.00000 0.376473
$$255$$ 0 0
$$256$$ 19.0000 1.18750
$$257$$ −9.79796 9.79796i −0.611180 0.611180i 0.332074 0.943253i $$-0.392252\pi$$
−0.943253 + 0.332074i $$0.892252\pi$$
$$258$$ −22.0454 + 22.0454i −1.37249 + 1.37249i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 18.0000i 1.11417i
$$262$$ −14.6969 + 14.6969i −0.907980 + 0.907980i
$$263$$ −17.1464 + 17.1464i −1.05729 + 1.05729i −0.0590383 + 0.998256i $$0.518803\pi$$
−0.998256 + 0.0590383i $$0.981197\pi$$
$$264$$ 3.00000i 0.184637i
$$265$$ 0 0
$$266$$ 12.0000i 0.735767i
$$267$$ −14.6969 14.6969i −0.899438 0.899438i
$$268$$ 2.44949 + 2.44949i 0.149626 + 0.149626i
$$269$$ 24.0000 1.46331 0.731653 0.681677i $$-0.238749\pi$$
0.731653 + 0.681677i $$0.238749\pi$$
$$270$$ 0 0
$$271$$ 2.00000 0.121491 0.0607457 0.998153i $$-0.480652\pi$$
0.0607457 + 0.998153i $$0.480652\pi$$
$$272$$ −24.4949 24.4949i −1.48522 1.48522i
$$273$$ −14.6969 14.6969i −0.889499 0.889499i
$$274$$ 24.0000i 1.44989i
$$275$$ 0 0
$$276$$ 12.0000i 0.722315i
$$277$$ −12.2474 + 12.2474i −0.735878 + 0.735878i −0.971777 0.235900i $$-0.924196\pi$$
0.235900 + 0.971777i $$0.424196\pi$$
$$278$$ 26.9444 26.9444i 1.61602 1.61602i
$$279$$ 12.0000i 0.718421i
$$280$$ 0 0
$$281$$ 30.0000i 1.78965i −0.446417 0.894825i $$-0.647300\pi$$
0.446417 0.894825i $$-0.352700\pi$$
$$282$$ 14.6969 14.6969i 0.875190 0.875190i
$$283$$ 12.2474 + 12.2474i 0.728035 + 0.728035i 0.970228 0.242193i $$-0.0778667\pi$$
−0.242193 + 0.970228i $$0.577867\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 6.00000 0.354787
$$287$$ 14.6969 + 14.6969i 0.867533 + 0.867533i
$$288$$ 11.0227 11.0227i 0.649519 0.649519i
$$289$$ 31.0000i 1.82353i
$$290$$ 0 0
$$291$$ −24.0000 −1.40690
$$292$$ −2.44949 + 2.44949i −0.143346 + 0.143346i
$$293$$ 9.79796 9.79796i 0.572403 0.572403i −0.360396 0.932799i $$-0.617359\pi$$
0.932799 + 0.360396i $$0.117359\pi$$
$$294$$ −15.0000 −0.874818
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.67423 + 3.67423i 0.213201 + 0.213201i
$$298$$ 7.34847 + 7.34847i 0.425685 + 0.425685i
$$299$$ −24.0000 −1.38796
$$300$$ 0 0
$$301$$ −36.0000 −2.07501
$$302$$ −12.2474 12.2474i −0.704761 0.704761i
$$303$$ −22.0454 + 22.0454i −1.26648 + 1.26648i
$$304$$ 10.0000i 0.573539i
$$305$$ 0 0
$$306$$ −36.0000 −2.05798
$$307$$ −17.1464 + 17.1464i −0.978598 + 0.978598i −0.999776 0.0211774i $$-0.993259\pi$$
0.0211774 + 0.999776i $$0.493259\pi$$
$$308$$ 2.44949 2.44949i 0.139573 0.139573i
$$309$$ 6.00000i 0.341328i
$$310$$ 0 0
$$311$$ 24.0000i 1.36092i 0.732787 + 0.680458i $$0.238219\pi$$
−0.732787 + 0.680458i $$0.761781\pi$$
$$312$$ 7.34847 + 7.34847i 0.416025 + 0.416025i
$$313$$ −4.89898 4.89898i −0.276907 0.276907i 0.554966 0.831873i $$-0.312731\pi$$
−0.831873 + 0.554966i $$0.812731\pi$$
$$314$$ 24.0000 1.35440
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ −4.89898 4.89898i −0.275154 0.275154i 0.556017 0.831171i $$-0.312329\pi$$
−0.831171 + 0.556017i $$0.812329\pi$$
$$318$$ −14.6969 14.6969i −0.824163 0.824163i
$$319$$ 6.00000i 0.335936i
$$320$$ 0 0
$$321$$ 6.00000i 0.334887i
$$322$$ −29.3939 + 29.3939i −1.63806 + 1.63806i
$$323$$ −9.79796 + 9.79796i −0.545173 + 0.545173i
$$324$$ 9.00000i 0.500000i
$$325$$ 0 0
$$326$$ 30.0000i 1.66155i
$$327$$ 12.2474 12.2474i 0.677285 0.677285i
$$328$$ −7.34847 7.34847i −0.405751 0.405751i
$$329$$ 24.0000 1.32316
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 7.34847 + 7.34847i 0.403300 + 0.403300i
$$333$$ 0 0
$$334$$ 6.00000i 0.328305i
$$335$$ 0 0
$$336$$ 30.0000 1.63663
$$337$$ 22.0454 22.0454i 1.20089 1.20089i 0.226994 0.973896i $$-0.427110\pi$$
0.973896 0.226994i $$-0.0728897\pi$$
$$338$$ −1.22474 + 1.22474i −0.0666173 + 0.0666173i
$$339$$ −12.0000 −0.651751
$$340$$ 0 0
$$341$$ 4.00000i 0.216612i
$$342$$ −7.34847 7.34847i −0.397360 0.397360i
$$343$$ 4.89898 + 4.89898i 0.264520 + 0.264520i
$$344$$ 18.0000 0.970495
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12.2474 + 12.2474i 0.657477 + 0.657477i 0.954783 0.297305i $$-0.0960878\pi$$
−0.297305 + 0.954783i $$0.596088\pi$$
$$348$$ −7.34847 + 7.34847i −0.393919 + 0.393919i
$$349$$ 2.00000i 0.107058i −0.998566 0.0535288i $$-0.982953\pi$$
0.998566 0.0535288i $$-0.0170469\pi$$
$$350$$ 0 0
$$351$$ 18.0000 0.960769
$$352$$ −3.67423 + 3.67423i −0.195837 + 0.195837i
$$353$$ 24.4949 24.4949i 1.30373 1.30373i 0.377875 0.925856i $$-0.376655\pi$$
0.925856 0.377875i $$-0.123345\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 12.0000i 0.635999i
$$357$$ −29.3939 29.3939i −1.55569 1.55569i
$$358$$ 0 0
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ 15.0000 0.789474
$$362$$ −12.2474 12.2474i −0.643712 0.643712i
$$363$$ −1.22474 1.22474i −0.0642824 0.0642824i
$$364$$ 12.0000i 0.628971i
$$365$$ 0 0
$$366$$ 6.00000i 0.313625i
$$367$$ 2.44949 2.44949i 0.127862 0.127862i −0.640280 0.768142i $$-0.721182\pi$$
0.768142 + 0.640280i $$0.221182\pi$$
$$368$$ 24.4949 24.4949i 1.27688 1.27688i
$$369$$ −18.0000 −0.937043
$$370$$ 0 0
$$371$$ 24.0000i 1.24602i
$$372$$ −4.89898 + 4.89898i −0.254000 + 0.254000i
$$373$$ 17.1464 + 17.1464i 0.887808 + 0.887808i 0.994312 0.106504i $$-0.0339657\pi$$
−0.106504 + 0.994312i $$0.533966\pi$$
$$374$$ 12.0000 0.620505
$$375$$ 0 0
$$376$$ −12.0000 −0.618853
$$377$$ −14.6969 14.6969i −0.756931 0.756931i
$$378$$ 22.0454 22.0454i 1.13389 1.13389i
$$379$$ 20.0000i 1.02733i −0.857991 0.513665i $$-0.828287\pi$$
0.857991 0.513665i $$-0.171713\pi$$
$$380$$ 0 0
$$381$$ −6.00000 −0.307389
$$382$$ 29.3939 29.3939i 1.50392 1.50392i
$$383$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$384$$ −21.0000 −1.07165
$$385$$ 0 0
$$386$$ 18.0000i 0.916176i
$$387$$ 22.0454 22.0454i 1.12063 1.12063i
$$388$$ −9.79796 9.79796i −0.497416 0.497416i
$$389$$ −12.0000 −0.608424 −0.304212 0.952604i $$-0.598393\pi$$
−0.304212 + 0.952604i $$0.598393\pi$$
$$390$$ 0 0
$$391$$ −48.0000 −2.42746
$$392$$ 6.12372 + 6.12372i 0.309295 + 0.309295i
$$393$$ 14.6969 14.6969i 0.741362 0.741362i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 3.00000i 0.150756i
$$397$$ 4.89898 4.89898i 0.245873 0.245873i −0.573402 0.819274i $$-0.694377\pi$$
0.819274 + 0.573402i $$0.194377\pi$$
$$398$$ −4.89898 + 4.89898i −0.245564 + 0.245564i
$$399$$ 12.0000i 0.600751i
$$400$$ 0 0
$$401$$ 24.0000i 1.19850i −0.800561 0.599251i $$-0.795465\pi$$
0.800561 0.599251i $$-0.204535\pi$$
$$402$$ −7.34847 7.34847i −0.366508 0.366508i
$$403$$ −9.79796 9.79796i −0.488071 0.488071i
$$404$$ −18.0000 −0.895533
$$405$$ 0 0
$$406$$ −36.0000 −1.78665
$$407$$ 0 0
$$408$$ 14.6969 + 14.6969i 0.727607 + 0.727607i
$$409$$ 10.0000i 0.494468i 0.968956 + 0.247234i $$0.0795217\pi$$
−0.968956 + 0.247234i $$0.920478\pi$$
$$410$$ 0 0
$$411$$ 24.0000i 1.18383i
$$412$$ 2.44949 2.44949i 0.120678 0.120678i
$$413$$ 0 0
$$414$$ 36.0000i 1.76930i
$$415$$ 0 0
$$416$$ 18.0000i 0.882523i
$$417$$ −26.9444 + 26.9444i −1.31947 + 1.31947i
$$418$$ 2.44949 + 2.44949i 0.119808 + 0.119808i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −31.8434 31.8434i −1.55011 1.55011i
$$423$$ −14.6969 + 14.6969i −0.714590 + 0.714590i
$$424$$ 12.0000i 0.582772i
$$425$$ 0 0
$$426$$ −36.0000 −1.74421
$$427$$ 4.89898 4.89898i 0.237078 0.237078i
$$428$$ −2.44949 + 2.44949i −0.118401 + 0.118401i
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ 24.0000i 1.15604i −0.816023 0.578020i $$-0.803826\pi$$
0.816023 0.578020i $$-0.196174\pi$$
$$432$$ −18.3712 + 18.3712i −0.883883 + 0.883883i
$$433$$ 19.5959 + 19.5959i 0.941720 + 0.941720i 0.998393 0.0566731i $$-0.0180493\pi$$
−0.0566731 + 0.998393i $$0.518049\pi$$
$$434$$ −24.0000 −1.15204
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ −9.79796 9.79796i −0.468700 0.468700i
$$438$$ 7.34847 7.34847i 0.351123 0.351123i
$$439$$ 26.0000i 1.24091i 0.784241 + 0.620456i $$0.213053\pi$$
−0.784241 + 0.620456i $$0.786947\pi$$
$$440$$ 0 0
$$441$$ 15.0000 0.714286
$$442$$ 29.3939 29.3939i 1.39812 1.39812i
$$443$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 42.0000i 1.98876i
$$447$$ −7.34847 7.34847i −0.347571 0.347571i
$$448$$ −2.44949 2.44949i −0.115728 0.115728i
$$449$$ −12.0000 −0.566315 −0.283158 0.959073i $$-0.591382\pi$$
−0.283158 + 0.959073i $$0.591382\pi$$
$$450$$ 0 0
$$451$$ 6.00000 0.282529
$$452$$ −4.89898 4.89898i −0.230429 0.230429i
$$453$$ 12.2474 + 12.2474i 0.575435 + 0.575435i
$$454$$ 30.0000i 1.40797i
$$455$$ 0 0
$$456$$ 6.00000i 0.280976i
$$457$$ −22.0454 + 22.0454i −1.03124 + 1.03124i −0.0317447 + 0.999496i $$0.510106\pi$$
−0.999496 + 0.0317447i $$0.989894\pi$$
$$458$$ 12.2474 12.2474i 0.572286 0.572286i
$$459$$ 36.0000 1.68034
$$460$$ 0 0
$$461$$ 6.00000i 0.279448i −0.990190 0.139724i $$-0.955378\pi$$
0.990190 0.139724i $$-0.0446215\pi$$
$$462$$ −7.34847 + 7.34847i −0.341882 + 0.341882i
$$463$$ −2.44949 2.44949i −0.113837 0.113837i 0.647893 0.761731i $$-0.275650\pi$$
−0.761731 + 0.647893i $$0.775650\pi$$
$$464$$ 30.0000 1.39272
$$465$$ 0 0
$$466$$ 12.0000 0.555889
$$467$$ 24.4949 + 24.4949i 1.13349 + 1.13349i 0.989593 + 0.143896i $$0.0459630\pi$$
0.143896 + 0.989593i $$0.454037\pi$$
$$468$$ 7.34847 + 7.34847i 0.339683 + 0.339683i
$$469$$ 12.0000i 0.554109i
$$470$$ 0 0
$$471$$ −24.0000 −1.10586
$$472$$ 0 0
$$473$$ −7.34847 + 7.34847i −0.337883 + 0.337883i
$$474$$ −30.0000 −1.37795
$$475$$ 0 0
$$476$$ 24.0000i 1.10004i
$$477$$ 14.6969 + 14.6969i 0.672927 + 0.672927i
$$478$$ 0 0
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 12.2474 + 12.2474i 0.557856 + 0.557856i
$$483$$ 29.3939 29.3939i 1.33747 1.33747i
$$484$$ 1.00000i 0.0454545i
$$485$$ 0 0
$$486$$ 27.0000i 1.22474i
$$487$$ −17.1464 + 17.1464i −0.776979 + 0.776979i −0.979316 0.202337i $$-0.935146\pi$$
0.202337 + 0.979316i $$0.435146\pi$$
$$488$$ −2.44949 + 2.44949i −0.110883 + 0.110883i
$$489$$ 30.0000i 1.35665i
$$490$$ 0 0
$$491$$ 12.0000i 0.541552i 0.962642 + 0.270776i $$0.0872803\pi$$
−0.962642 + 0.270776i $$0.912720\pi$$
$$492$$ −7.34847 7.34847i −0.331295 0.331295i
$$493$$ −29.3939 29.3939i −1.32383 1.32383i
$$494$$ 12.0000 0.539906
$$495$$ 0 0
$$496$$ 20.0000 0.898027
$$497$$ −29.3939 29.3939i −1.31850 1.31850i
$$498$$ −22.0454 22.0454i −0.987878 0.987878i
$$499$$ 16.0000i 0.716258i −0.933672 0.358129i $$-0.883415\pi$$
0.933672 0.358129i $$-0.116585\pi$$
$$500$$ 0 0
$$501$$ 6.00000i 0.268060i
$$502$$ 14.6969 14.6969i 0.655956 0.655956i
$$503$$ −17.1464 + 17.1464i −0.764521 + 0.764521i −0.977136 0.212615i $$-0.931802\pi$$
0.212615 + 0.977136i $$0.431802\pi$$
$$504$$ −18.0000 −0.801784
$$505$$ 0 0
$$506$$ 12.0000i 0.533465i
$$507$$ 1.22474 1.22474i 0.0543928 0.0543928i
$$508$$ −2.44949 2.44949i −0.108679 0.108679i
$$509$$ 24.0000 1.06378 0.531891 0.846813i $$-0.321482\pi$$
0.531891 + 0.846813i $$0.321482\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ −6.12372 6.12372i −0.270633 0.270633i
$$513$$ 7.34847 + 7.34847i 0.324443 + 0.324443i
$$514$$ 24.0000i 1.05859i
$$515$$ 0 0
$$516$$ 18.0000 0.792406
$$517$$ 4.89898 4.89898i 0.215457 0.215457i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 24.0000i 1.05146i −0.850652 0.525730i $$-0.823792\pi$$
0.850652 0.525730i $$-0.176208\pi$$
$$522$$ 22.0454 22.0454i 0.964901 0.964901i
$$523$$ 7.34847 + 7.34847i 0.321326 + 0.321326i 0.849276 0.527950i $$-0.177039\pi$$
−0.527950 + 0.849276i $$0.677039\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 42.0000 1.83129
$$527$$ −19.5959 19.5959i −0.853612 0.853612i
$$528$$ 6.12372 6.12372i 0.266501 0.266501i
$$529$$ 25.0000i 1.08696i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 4.89898 4.89898i 0.212398 0.212398i
$$533$$ 14.6969 14.6969i 0.636595 0.636595i
$$534$$ 36.0000i 1.55787i
$$535$$ 0 0
$$536$$ 6.00000i 0.259161i
$$537$$ 0 0
$$538$$ −29.3939 29.3939i −1.26726 1.26726i
$$539$$ −5.00000 −0.215365
$$540$$ 0 0
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ −2.44949 2.44949i −0.105215 0.105215i
$$543$$ 12.2474 + 12.2474i 0.525588 + 0.525588i
$$544$$ 36.0000i 1.54349i
$$545$$ 0 0
$$546$$ 36.0000i 1.54066i
$$547$$ −12.2474 + 12.2474i −0.523663 + 0.523663i −0.918676 0.395013i $$-0.870740\pi$$
0.395013 + 0.918676i $$0.370740\pi$$
$$548$$ −9.79796 + 9.79796i −0.418548 + 0.418548i
$$549$$ 6.00000i 0.256074i
$$550$$ 0 0
$$551$$ 12.0000i 0.511217i
$$552$$ −14.6969 + 14.6969i −0.625543 + 0.625543i
$$553$$ −24.4949 24.4949i −1.04163 1.04163i
$$554$$ 30.0000 1.27458
$$555$$ 0 0
$$556$$ −22.0000 −0.933008
$$557$$ −19.5959 19.5959i −0.830306 0.830306i 0.157253 0.987558i $$-0.449736\pi$$
−0.987558 + 0.157253i $$0.949736\pi$$
$$558$$ 14.6969 14.6969i 0.622171 0.622171i
$$559$$ 36.0000i 1.52264i
$$560$$ 0 0
$$561$$ −12.0000 −0.506640
$$562$$ −36.7423 + 36.7423i −1.54988 + 1.54988i
$$563$$ 7.34847 7.34847i 0.309701 0.309701i −0.535092 0.844794i $$-0.679723\pi$$
0.844794 + 0.535092i $$0.179723\pi$$
$$564$$ −12.0000 −0.505291
$$565$$ 0 0
$$566$$ 30.0000i 1.26099i
$$567$$ −22.0454 + 22.0454i −0.925820 + 0.925820i
$$568$$ 14.6969 + 14.6969i 0.616670 + 0.616670i
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ 14.0000 0.585882 0.292941 0.956131i $$-0.405366\pi$$
0.292941 + 0.956131i $$0.405366\pi$$
$$572$$ −2.44949 2.44949i −0.102418 0.102418i
$$573$$ −29.3939 + 29.3939i −1.22795 + 1.22795i
$$574$$ 36.0000i 1.50261i
$$575$$ 0 0
$$576$$ 3.00000 0.125000
$$577$$ 14.6969 14.6969i 0.611842 0.611842i −0.331584 0.943426i $$-0.607583\pi$$
0.943426 + 0.331584i $$0.107583\pi$$
$$578$$ 37.9671 37.9671i 1.57922 1.57922i
$$579$$ 18.0000i 0.748054i
$$580$$ 0 0
$$581$$ 36.0000i 1.49353i
$$582$$ 29.3939 + 29.3939i 1.21842 + 1.21842i
$$583$$ −4.89898 4.89898i −0.202895 0.202895i
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ −24.0000 −0.991431
$$587$$ 4.89898 + 4.89898i 0.202203 + 0.202203i 0.800943 0.598741i $$-0.204332\pi$$
−0.598741 + 0.800943i $$0.704332\pi$$
$$588$$ 6.12372 + 6.12372i 0.252538 + 0.252538i
$$589$$ 8.00000i 0.329634i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −14.6969 + 14.6969i −0.603531 + 0.603531i −0.941248 0.337717i $$-0.890345\pi$$
0.337717 + 0.941248i $$0.390345\pi$$
$$594$$ 9.00000i 0.369274i
$$595$$ 0 0
$$596$$ 6.00000i 0.245770i
$$597$$ 4.89898 4.89898i 0.200502 0.200502i
$$598$$ 29.3939 + 29.3939i 1.20201 + 1.20201i
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 44.0908 + 44.0908i 1.79701 + 1.79701i
$$603$$ 7.34847 + 7.34847i 0.299253 + 0.299253i
$$604$$ 10.0000i 0.406894i
$$605$$ 0 0
$$606$$ 54.0000 2.19360
$$607$$ 12.2474 12.2474i 0.497109 0.497109i −0.413428 0.910537i $$-0.635669\pi$$
0.910537 + 0.413428i $$0.135669\pi$$
$$608$$ −7.34847 + 7.34847i −0.298020 + 0.298020i
$$609$$ 36.0000 1.45879
$$610$$ 0 0
$$611$$ 24.0000i 0.970936i
$$612$$ 14.6969 + 14.6969i 0.594089 + 0.594089i
$$613$$ −2.44949 2.44949i −0.0989340 0.0989340i 0.655907 0.754841i $$-0.272286\pi$$
−0.754841 + 0.655907i $$0.772286\pi$$
$$614$$ 42.0000 1.69498
$$615$$ 0 0
$$616$$ 6.00000 0.241747
$$617$$ −14.6969 14.6969i −0.591676 0.591676i 0.346408 0.938084i $$-0.387401\pi$$
−0.938084 + 0.346408i $$0.887401\pi$$
$$618$$ −7.34847 + 7.34847i −0.295599 + 0.295599i
$$619$$ 4.00000i 0.160774i −0.996764 0.0803868i $$-0.974384\pi$$
0.996764 0.0803868i $$-0.0256155\pi$$
$$620$$ 0 0
$$621$$ 36.0000i 1.44463i
$$622$$ 29.3939 29.3939i 1.17859 1.17859i
$$623$$ −29.3939 + 29.3939i −1.17764 + 1.17764i
$$624$$ 30.0000i 1.20096i
$$625$$ 0 0
$$626$$ 12.0000i 0.479616i
$$627$$ −2.44949 2.44949i −0.0978232 0.0978232i
$$628$$ −9.79796 9.79796i −0.390981 0.390981i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 12.2474 + 12.2474i 0.487177 + 0.487177i
$$633$$ 31.8434 + 31.8434i 1.26566 + 1.26566i
$$634$$ 12.0000i 0.476581i
$$635$$ 0 0
$$636$$ 12.0000i 0.475831i
$$637$$ −12.2474 + 12.2474i −0.485262 + 0.485262i
$$638$$ −7.34847 + 7.34847i −0.290929 + 0.290929i
$$639$$ 36.0000 1.42414
$$640$$ 0 0
$$641$$ 12.0000i 0.473972i −0.971513 0.236986i $$-0.923841\pi$$
0.971513 0.236986i $$-0.0761595\pi$$
$$642$$ 7.34847 7.34847i 0.290021 0.290021i
$$643$$ 12.2474 + 12.2474i 0.482992 + 0.482992i 0.906086 0.423094i $$-0.139056\pi$$
−0.423094 + 0.906086i $$0.639056\pi$$
$$644$$ 24.0000 0.945732
$$645$$ 0 0
$$646$$ 24.0000 0.944267
$$647$$ −19.5959 19.5959i −0.770395 0.770395i 0.207780 0.978175i $$-0.433376\pi$$
−0.978175 + 0.207780i $$0.933376\pi$$
$$648$$ 11.0227 11.0227i 0.433013 0.433013i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 24.0000 0.940634
$$652$$ −12.2474 + 12.2474i −0.479647 + 0.479647i
$$653$$ −29.3939 + 29.3939i −1.15027 + 1.15027i −0.163773 + 0.986498i $$0.552367\pi$$
−0.986498 + 0.163773i $$0.947633\pi$$
$$654$$ −30.0000 −1.17309
$$655$$ 0 0
$$656$$ 30.0000i 1.17130i
$$657$$ −7.34847 + 7.34847i −0.286691 + 0.286691i
$$658$$ −29.3939 29.3939i −1.14589 1.14589i
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ 34.0000 1.32245 0.661223 0.750189i $$-0.270038\pi$$
0.661223 + 0.750189i $$0.270038\pi$$
$$662$$ 34.2929 + 34.2929i 1.33283 + 1.33283i
$$663$$ −29.3939 + 29.3939i −1.14156 + 1.14156i
$$664$$ 18.0000i 0.698535i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 29.3939 29.3939i 1.13814 1.13814i
$$668$$ −2.44949 + 2.44949i −0.0947736 + 0.0947736i
$$669$$ 42.0000i 1.62381i
$$670$$ 0 0
$$671$$ 2.00000i 0.0772091i
$$672$$ −22.0454 22.0454i −0.850420 0.850420i
$$673$$ 2.44949 + 2.44949i 0.0944209 + 0.0944209i 0.752739 0.658319i $$-0.228732\pi$$
−0.658319 + 0.752739i $$0.728732\pi$$
$$674$$ −54.0000 −2.08000
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$678$$ 14.6969 + 14.6969i 0.564433 + 0.564433i
$$679$$ 48.0000i 1.84207i
$$680$$ 0 0
$$681$$ 30.0000i 1.14960i
$$682$$ −4.89898 + 4.89898i −0.187592 + 0.187592i
$$683$$ −14.6969 + 14.6969i −0.562363 + 0.562363i −0.929978 0.367615i $$-0.880174\pi$$
0.367615 + 0.929978i $$0.380174\pi$$
$$684$$ 6.00000i 0.229416i
$$685$$ 0 0
$$686$$ 12.0000i 0.458162i
$$687$$ −12.2474 + 12.2474i −0.467269 + 0.467269i
$$688$$ −36.7423 36.7423i −1.40079 1.40079i
$$689$$ −24.0000 −0.914327
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 0 0
$$693$$ 7.34847 7.34847i 0.279145 0.279145i
$$694$$ 30.0000i 1.13878i
$$695$$ 0 0
$$696$$ −18.0000 −0.682288
$$697$$ 29.3939 29.3939i 1.11337 1.11337i
$$698$$ −2.44949 + 2.44949i −0.0927146 + 0.0927146i
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ 18.0000i 0.679851i 0.940452 + 0.339925i $$0.110402\pi$$
−0.940452 + 0.339925i $$0.889598\pi$$
$$702$$ −22.0454 22.0454i −0.832050 0.832050i
$$703$$ 0 0
$$704$$ −1.00000 −0.0376889
$$705$$ 0 0
$$706$$ −60.0000 −2.25813
$$707$$ 44.0908 + 44.0908i 1.65821 + 1.65821i
$$708$$ 0 0
$$709$$ 46.0000i 1.72757i 0.503864 + 0.863783i $$0.331911\pi$$
−0.503864 + 0.863783i $$0.668089\pi$$
$$710$$ 0 0
$$711$$ 30.0000 1.12509
$$712$$ 14.6969 14.6969i 0.550791 0.550791i
$$713$$ 19.5959 19.5959i 0.733873 0.733873i
$$714$$ 72.0000i 2.69453i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 29.3939 + 29.3939i 1.09697 + 1.09697i
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ −12.0000 −0.446903
$$722$$ −18.3712 18.3712i −0.683704 0.683704i
$$723$$ −12.2474 12.2474i −0.455488 0.455488i
$$724$$ 10.0000i 0.371647i
$$725$$ 0 0
$$726$$ 3.00000i 0.111340i
$$727$$ 22.0454 22.0454i 0.817619 0.817619i −0.168144 0.985763i $$-0.553777\pi$$
0.985763 + 0.168144i $$0.0537772\pi$$
$$728$$ 14.6969 14.6969i 0.544705 0.544705i
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 72.0000i 2.66302i
$$732$$ −2.44949 + 2.44949i −0.0905357 + 0.0905357i
$$733$$ −22.0454 22.0454i −0.814266 0.814266i 0.171005 0.985270i $$-0.445299\pi$$
−0.985270 + 0.171005i $$0.945299\pi$$
$$734$$ −6.00000 −0.221464
$$735$$ 0 0
$$736$$ −36.0000 −1.32698
$$737$$ −2.44949 2.44949i −0.0902281 0.0902281i
$$738$$ 22.0454 + 22.0454i 0.811503 + 0.811503i
$$739$$ 38.0000i 1.39785i −0.715194 0.698926i $$-0.753662\pi$$
0.715194 0.698926i $$-0.246338\pi$$
$$740$$ 0 0
$$741$$ −12.0000 −0.440831
$$742$$ −29.3939 + 29.3939i −1.07908 + 1.07908i
$$743$$ 12.2474 12.2474i 0.449315 0.449315i −0.445812 0.895127i $$-0.647085\pi$$
0.895127 + 0.445812i $$0.147085\pi$$
$$744$$ −12.0000 −0.439941
$$745$$ 0 0
$$746$$ 42.0000i 1.53773i
$$747$$ 22.0454 + 22.0454i 0.806599 + 0.806599i
$$748$$ −4.89898 4.89898i −0.179124 0.179124i
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ 4.00000 0.145962 0.0729810 0.997333i $$-0.476749\pi$$
0.0729810 + 0.997333i $$0.476749\pi$$
$$752$$ 24.4949 + 24.4949i 0.893237 + 0.893237i
$$753$$ −14.6969 + 14.6969i −0.535586 + 0.535586i
$$754$$ 36.0000i 1.31104i
$$755$$ 0 0
$$756$$ −18.0000 −0.654654
$$757$$ 9.79796 9.79796i 0.356113 0.356113i −0.506265 0.862378i $$-0.668974\pi$$
0.862378 + 0.506265i $$0.168974\pi$$
$$758$$ −24.4949 + 24.4949i −0.889695 + 0.889695i
$$759$$ 12.0000i 0.435572i
$$760$$ 0 0
$$761$$ 42.0000i 1.52250i −0.648459 0.761249i $$-0.724586\pi$$
0.648459 0.761249i $$-0.275414\pi$$
$$762$$ 7.34847 + 7.34847i 0.266207 + 0.266207i
$$763$$ −24.4949 24.4949i −0.886775 0.886775i
$$764$$ −24.0000 −0.868290
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 23.2702 + 23.2702i 0.839689 + 0.839689i
$$769$$ 22.0000i 0.793340i −0.917961 0.396670i $$-0.870166\pi$$
0.917961 0.396670i $$-0.129834\pi$$
$$770$$ 0 0
$$771$$ 24.0000i 0.864339i
$$772$$ −7.34847 + 7.34847i −0.264477 + 0.264477i
$$773$$ 19.5959 19.5959i 0.704816 0.704816i −0.260624 0.965440i $$-0.583928\pi$$
0.965440 + 0.260624i $$0.0839283\pi$$
$$774$$ −54.0000 −1.94099
$$775$$ 0 0
$$776$$ 24.0000i 0.861550i
$$777$$ 0 0
$$778$$ 14.6969 + 14.6969i 0.526911 + 0.526911i
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ −12.0000 −0.429394
$$782$$ 58.7878 + 58.7878i 2.10225 + 2.10225i
$$783$$ −22.0454 + 22.0454i −0.787839 + 0.787839i
$$784$$ 25.0000i 0.892857i
$$785$$ 0 0
$$786$$ −36.0000 −1.28408
$$787$$ −2.44949 + 2.44949i −0.0873149 + 0.0873149i −0.749415 0.662100i $$-0.769665\pi$$
0.662100 + 0.749415i $$0.269665\pi$$
$$788$$ 0 0
$$789$$ −42.0000 −1.49524